Can I be sued by my old apartment for breaking my lease to buy my house?

You can be sued by the landlord for breaking your lease even though you did so to buy a house.

If you did not give the required notice before vacating the premises, you are liable for the rent until the apartment is re-rented.  If the apartment is not re-rented, you are liable for the rent for the balance of the term of your lease.  The landlord cannot allow the apartment to remain vacant for the balance of the term of the lease.  The landlord must mitigate (minimize) damages by making reasonable efforts to find another tenant. If the landlord fails to mitigate damages,  the landlord's damages (the amount the landlord is seeking to recover in a lawsuit) will be reduced accordingly.  Reasonable efforts on the part of the landlord would be determined by what other landlords in the area are doing to attract tenants; for example, posting a sign on the property advertising the vacancy, advertising the vacancy in the newspaper or a local rental guide, etc.

If the apartment is re-rented prior to the end of your tenancy, your obligation to pay rent ends.  However, if the new tenant is paying less rent than you were paying under your lease, you would remain liable for the difference in rent for the balance of the term of your lease.  Again, the landlord must mitigate damages and must have a very good reason as to why the new tenant is paying less rent than you were paying.  For example, market conditions may justify the reduced rent.  If the landlord does not have justification for the reduced rent, the landlord failed to mitigate damages and the landlord's damages will be reduced accordingly (landlord may not be able to hold you liable for the disparity in rent for the balance of the term of your lease).